Pythagorean Theorem (Finding the Hypotenuse)

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

What is the formula for finding the hypotenuse?

Back

The formula for finding the hypotenuse (c) in a right triangle is a² + b² = c².

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

Front

What is the length of the hypotenuse if the two other sides are 5 cm and 12 cm?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √169 = 13 cm.

Front

Find the missing side if the hypotenuse is 13 and one side is 5.

Back

Using the Pythagorean Theorem: 13² = 5² + b², 169 = 25 + b², b² = 144, so b = √144 = 12.

Front

What is the length of the hypotenuse if the sides are 9 and 12?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225, so c = √225 = 15.

Front

If the hypotenuse is 15 and one side is 9, what is the length of the other side?

Back

Using the Pythagorean Theorem: 15² = 9² + b², 225 = 81 + b², b² = 144, so b = √144 = 12.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a right triangle has sides of length 7 and 24, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 7² + 24² = 49 + 576 = 625, so c = √625 = 25.

Front

What is the Pythagorean Theorem used for?

Back

The Pythagorean Theorem is used to find the length of a side in a right triangle when the lengths of the other two sides are known.